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Reference [11] investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to…
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…
We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Partitioning is a fundamental challenge for non-centralized control of large-scale systems, such as hierarchical, decentralized, distributed, and coalitional strategies. The problem consists of finding a decomposition of a network of…
We consider distributed optimization problems in which a group of agents are to collaboratively seek the global optimum through peer-to-peer communication networks. The problem arises in various application areas, such as resource…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits…
We present a new primal-dual splitting algorithm for structured monotone inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of our framework, which is motivated by image recovery applications, is to consider…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…